This paper examines some of the criteria commonly used to predict the initiation of fracture during cold forming utilizing the existing test data on low carbon steels. A limiting condition based on integrals of stress functions, which takes into account the tensile stress ratio and triaxiality is proposed, and its applicability demonstrated with test data of low carbon steel of different heats is developed. Material fracture can be estimated during cold forming by adding the proposed criterion to the finite element computer programs. The method of evaluation of the material constants in the proposed criterion is developed and demonstrated. By this way, the traditional procedures of trial and error, which involve cost and time, can be minimized.